L. Stenflo, M. Marklund, G. Brodin, P. K. Shukla
Nonlinear oscillations within a plasma slab are analyzed. Two types of solutions are found, depending on the initial value of the electron density. The first represents regular oscillations within the plasma slab, while the second gives rise to explosive growth at the slab centre or at the edges. The results are discussed.
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The analytical solution of the boundary problem on behaviour (oscillations) of the electronic plasmas with arbitrary degree of degeneration of electronic gas in a slab of the conducting medium is received. The kinetic Vlasov---Boltzmann equation with integral of collisions type BGK (Bhatnagar, Gross and Krook) and Maxwell equation for electric field are applied. Mirror (reflections) boundary conditions are used.
Doppler reflectometry is considered in slab plasma model in the frameworks of analytical theory. The diagnostics locality is analyzed for both regimes: linear and nonlinear in turbulence amplitude. The toroidal antenna focusing of probing beam to the cut-off is proposed and discussed as a method to increase diagnostics spatial resolution. It is shown that even in the case of nonlinear regime of multiple scattering, the diagnostics can be used for an estimation (with certain accuracy) of plasma poloidal rotation profile.
A generalized linear dispersion relation of electromagnetic slab universal modes is derived, taking into account arbitrary ion charge state, electron finite Larmor radius (FLR) effects, and Debye shielding effects. As a consequence, it provides more accurate predictions and is applicable to a wider range of plasmas. We find that electron FLR effects have a weakly stabilizing effect on the slab universal instability in electron-ion plasma, while Debye shielding strongly stabilizes this instability when $λ_D$ approaches $ρ_i$ ($λ_D$ is the Debye length and $ρ_i$ is the ion gyro-radius). In parti…
The existence of magnetosonic solitons in dusty plasmas is investigated. The nonlinear magnetohydrodynamic equations for a warm dusty magnetoplasma are thus derived. A solution of the nonlinear equations is presented. It is shown that, due to the presence of dust, static structures are allowed. This is in sharp contrast to the formation of the so called shocklets in usual magnetoplasmas. A comparatively small number of dust particles can thus drastically alter the behavior of the nonlinear structures in magnetized plasmas.
Magnetic reconnection is a fundamental plasma process associated with conversion of the embedded magnetic field energy into kinetic and thermal plasma energy, via bulk acceleration and Ohmic dissipation. In many high-energy astrophysical events, magnetic reconnection is invoked to explain the non-thermal signatures. However, the processes by which field energy is transferred to the plasma to power the observed emission are still not properly understood. Here, via 3D particle-in-cell simulations of a readily available (TW-mJ-class) laser interacting with a micro-scale plasma slab, we show that …
Magnetized laser-produced plasmas are central to many novel laboratory astrophysics and inertial confinement fusion studies, as well as in industrial applications. Here we provide the first complete description of the three-dimensional dynamics of a laser-driven plasma plume expanding in a 20 T transverse magnetic field. The plasma is collimated by the magnetic field into a slender, rapidly elongating slab, whose plasma-vacuum interface is unstable to the growth of the "classical", fluid-like magnetized Rayleigh-Taylor instability.
The passage of a magnetosonic (MS) soliton in a cold plasma leads to the displacement of charged particles in the direction of a compressive pulse and in the opposite direction of a rarefaction pulse. In the overdense plasma limit, the displacement induced by a weakly nonlinear MS soliton is derived analytically. This result is then used to derive an asymptotic expansion for the displacement resulting from the bouncing motion of a MS soliton reflected back and forth in a vacuum-bounded cold plasma slab. Particles' displacement after the pulse energy has been lost to the vacuum region is shown …
Suppression of power losses during laser pulse propagation in underdense plasma slab
本研究通过二维PIC模拟揭示中低密度、非相对论条件下前向拉曼散射主导激光损耗，并提出以频率失谐大于等离子体频率的多色激光抑制该散射、实现高效功率传输。
The nonlinear evolution of electromagnetic instabilities driven by the interpenetration of two $e^-\,e^+$ plasma clouds is explored using {\it ab initio} kinetic plasma simulations. We show that the plasma clouds slow down due to both oblique and Weibel generated electromagnetic fields, which deflect the particle trajectories, transferring bulk forward momentum into transverse momentum and thermal velocity spread. This process causes the flow velocity $v_{inst}$ to decrease approximately by a factor of $\sqrt{1/3}$ in a time interval $Δt_{αB} ω_p \sim c/(v_{fl}\sqrt{α_B})$, where $α_B$ is the …
Observational evidence in space and astrophysical plasmas with long collisional mean free path suggests that more massive charged particles may be preferentially heated. One possible mechanism for this is the turbulent cascade of energy from injection to dissipation scales, where the energy is converted to heat. Here we consider a simple system consisting of a magnetized plasma slab of electrons and a single ion species with a cross-field density gradient. We show that such a system is subject to an electron drift wave instability, known as the universal instability, which is stabilized only w…
Destabilization mechanism of the collisional microtearing mode in magnetized slab plasmas
本文结合理论分析与含综合碰撞模型的回旋动理学模拟，阐明电子温度梯度驱动的碰撞微撕裂模因平行感应电场滞后而失稳，并定量刻画其不稳定区及非线性磁重联特征。
Microtearing modes have been widely reported as a tearing parity electron temperature gradient driven plasma instability, which leads to fine scale tearing of the magnetic flux surfaces thereby resulting in reconnection of magnetic field lines and formation of magnetic islands. In slab geometry it has previously been shown that the drive mechanism requires a finite collision frequency. However, we find in linear gyrokinetic simulations that a collisionless fine-scale tearing parity instability exists even at low and zero collision frequency. Detailed studies reveal that these slab modes are al…
The generation of thin and high density plasma slabs at high repetition rate is a key issue for ultra-high intensity laser applications. We present a scheme to create such plasma slabs, based on the propagation and collision in a gas jet of two counter-propagating blast waves (BW). Each BW is launched by a sudden and local heating induced by a nanosecond laser beam that propagates along the side of the jet. The resulting cylindrical BW expands perpendicular to the beam. The shock front, bent by the gas jet density gradient, pushes and compresses the plasma toward the jet center. By using two p…
The adiabatic limit of a recently proposed dynamical extension of Taylor relaxation, \emph{multi-region relaxed magnetohydrodynamics} (MRxMHD) is summarized, with special attention to the appropriate definition of relative magnetic helicity. The formalism is illustrated using a simple two-region, sheared-magnetic-field model similar to the Hahm--Kulsrud--Taylor (HKT) rippled-boundary slab model. In MRxMHD a linear Grad--Shafranov equation applies, even at finite ripple amplitude. The adiabatic switching on of boundary ripple excites a shielding current sheet opposing reconnection at a resonant…
The problem of the linear microtearing mode in a slab magnetised plasma, and its connection to kinetic reconnecting modes, is addressed. Electrons are described using a novel hybrid fluid-kinetic model that captures electron heating, ions are gyrokinetic. Magnetic reconnection can occur as a result of either electron conductivity and inertia, depending on which one predominates. We eschew the use of an energy dependent collision frequency in the collisional operator model, unlike previous works. A model of the electron conductivity that matches the weakly collisional regime to the exact Landau…
Drift instabilities driven by slab ion temperature gradient in suprathermal plasmas
本文通过动力学方法研究Kappa分布等离子体中平板离子温度梯度驱动的漂移不稳定性，发现超热离子在大波数增强、小波数抑制不稳定性，并分析了密度不均匀性下的不稳定性边界。
It is shown that an overcritical density plasma slab can be totally transparent to a \textit{p}-polarized obliquely incident electromagnetic wave. High transparency is achieved due to the interference of the evanescent waves in the subcritical region. The transmission coefficient has the resonant character due to the excitation of a plasma surface mode (plasmon-polariton). It is crucial that two evanescent waves have certain phase shift to provide non-zero energy flux through non-transparent region. The required phase shift is obtained at the exact resonance and corresponds to the absolute tra…
The problem of collisionless plasma slab expansion into vacuum is solved within a two-temperature hydrodynamic approximation in the dispersionless limit of zero Debye radius. In the framework of such an approach, the solution by the Riemann method provides quite accurate description of the whole process of plasma dynamics. It is shown that the dispersionless approximation agrees very well with exact numerical solution of the full system of plasma hydrodynamic equations.
A three dimensional Particle-In-Cell simulation describing the interaction of an intense laser beam with a plasma slab is presented. It is observed that the laser generated electron current decays into magnetically isolated filaments. The filaments grow in scale and magnitude by a merging process in the course of which the field topology changes. The opposite process also takes place occasionally. The laser driven charge and energy flows and the reconnecting magnetic field mutually interact. At the end of the merging process flows and fields are confined close to the laser irradiated surface o…
In the present paper the linearized problem of plasma oscillations in slab (particularly, thin films) in external longitudinal alternating electric field is solved analytically. Specular boundary conditions of electron reflection from the plasma boundary are considered. Coefficients of continuous and discrete spectra of the problem are found, and electron distribution function on the plasma boundary and electric field are expressed in explicit form. Absorption of energy of electric field in slab is calculated.
Plasmon and polariton modes are derived for an ideal semi-infinite (half-space) plasma and an ideal plasma slab by using a general, unifying procedure, based on equations of motion, Maxwell's equations and suitable boundary conditions. Known results are re-obtained in much a more direct manner and new ones are derived. The approach consists of representing the charge disturbances by a displacement field in the positions of the moving particles (electrons). The dielectric response and the electron energy loss are computed. The surface contribution to the energy loss exhibits an oscillatory beha…
The properties of surface waves in the partially ionized, incompressible magnetized plasma slab are investigated in the present work. The waves are affected by the non ideal MHD effects which causes the finite drift of the magnetic field in the medium. When the finite drift of the magnetic field is ignored, the characteristics of the wave propagation in the partially ionized plasma fluid is similar to the ideal MHD except now the propagation properties depend on the fractional ionization of the medium. In the presence of Hall diffusion, the propagation of the sausage and kink surface waves dep…
Wave-particle interaction is a key process in particle diffusion in collisionless plasmas. We look into the interaction of single plasma waves with individual particles and discuss under which circumstances this is a chaotic process, leading to diffusion. We derive the equations of motion for a particle in the fields of a magnetostatic, circularly polarized, monochromatic wave and show that no chaotic particle motion can arise under such circumstances. A novel and exact analytic solution for the equations is presented. Additional plasma waves lead to a breakdown of the analytic solution and ch…
The heating of solar chromospheric inter-network regions by means of the absorption of electromagnetic (EM) waves that originate from the photospheric blackbody radiation is studied in the framework of a plasma slab model. The absorption is provided by the electron-neutral collisions in which electrons oscillate in the EM wave field and electron-neutral collisions damp the EM wave. Given the uncertain nature of the collision cross-section due to the plasma micro-turbulence, it is shown that for plausible physical parameters, the heating flux produced by the absorption of EM waves in the chromo…
Characterization of the stability and dynamics of a laser-produced plasma expanding across strong magnetic field
本研究通过大规模三维磁流体动力学模拟，探究了数十特斯拉横向磁场中激光产生等离子体的膨胀特性，揭示了磁化瑞利-泰勒不稳定性的结构作用及初始速度扰动引发的扭结运动对传播的影响，为相关领域研究提供了动力学依据。
Dual-decomposition multi-GPU particle-in-cell method for cylindrical plasmas: Batched Fourier-mode multigrid and balanced particle slabs
提出双分解多GPU粒子网格方法，通过傅里叶模式与粒子板分离及批量多重网格，实现高效求解与高扩展效率。
A gyrokinetic linear stability analysis of a collisionless slab geometry in the local approximation is presented. We focus on $k_\parallel=0$ universal (or entropy) modes driven by plasma gradients at small and large plasma $β$. These are small scale non-MHD instabilities with growth rates that typically peak near $k_\perpρ_i\sim 1$ and vanish in the long wavelength $k_\perp\to 0$ limit. This work also discusses a mode known as the Gradient Drift Coupling (GDC) instability previously reported in the gyrokinetic literature, which has a finite growth rate $γ= \sqrt{β/[2(1+β)]} C_s/|L_p|$ with $C…
Recently, warm dense matter (WDM) has emerged as an interdisciplinary field that draws increasing interest in plasma physics, condensed matter physics, high pressure science, astrophysics, inertial confinement fusion, as well as materials science under extreme conditions. To allow the study of well-defined WDM states, we have introduced the concept of idealized-slab plasmas that can be realized in the laboratory via (i) the isochoric heating of a solid and (ii) the propagation of a shock wave in a solid. The application of this concept provides new means for probing the dynamic conductivity, e…
Electromagnetic (EM) instabilities and turbulence driven by the electron-temperature gradient are considered in a local slab model of a tokamak-like plasma. The model describes perturbations at scales both larger and smaller than the flux-freezing scale $d_e$, and so captures both electrostatic and EM regimes of turbulence. The well-known electrostatic instabilities -- slab and curvature-mediated ETG -- are recovered, and a new instability is found in the EM regime, called the Thermo-Alfvénic instability (TAI). It exists in both a slab version (sTAI, destabilising kinetic Alfvén waves) and a c…
Collisionless Shock Acceleration of protons in a plasma slab produced in a gas jet by the collision of two laser-driven hydrodynamic shockwaves
本研究通过实验比较气体射流在无剪裁、单侧及双侧激光冲击波剪裁下的皮秒激光质子加速，证明双侧剪裁形成的近临界密度等离子体薄片可显著增强符合 CSA 机制的前向高能质子加速。
A set of reduced, 2-D, two-fluid, drift-MHD equations is derived. Using these equations, a complete and fully self-consistent solution is obtained for an isolated magnetic island propagating through a slab plasma with uniform but different ion and electron fluid velocities. The ion and electron fluid flow profiles around the island are uniquely determined, and are everywhere continuous. Moreover, the island phase-velocity is uniquely specified by the condition that there be zero net electromagnetic force acting on the island. Finally, the ion polarization current correction to the Rutherford i…
It is shown by particle-in-cell simulation that intense circularly polarized (CP) laser light can be contained in the cavity of a solid-density circular Al-plasma shell for hundreds of light-wave periods before it is dissipated by laser-plasma interaction. A right-hand CP laser pulse can propagate almost without reflection into the cavity through a highly magnetized overdense H-plasma slab filling the entrance hole. The entrapped laser light is then multiply reflected at the inner surfaces of the slab and shell plasmas, gradually losing energy to the latter. Compared to that of the incident la…
The tremendous applications of terahertz (THz) spectroscopy and imaging require THz sources in different parameters. We propose a novel scheme to generate single-cycle powerful THz pulses by ultrashort intense laser pulses incident obliquely on a tenuous plasma slab of few THz wavelengths in thickness. This is made possible by driving a large amplitude electron plasma wave in the plasma slab, thus producing a net transient current at the plasma surfaces. Theory and simulations show that such a THz source is capable of providing megawatt power and field strength of MV/cm, which may open up new …
In this paper, we obtain the dispersion relation for the lower-hybrid oscillations/waves in a cold magnetized electron-positron-ion (e-p-i) plasma. It is found that the frequency of the lower-hybrid oscillations in an e-p-i plasma is approximate $1/\sqrt{3}$ times the frequency of lower-hybrid oscillations in an electron-ion (e-i) plasma, provided the plasma density is high, and the equilibrium densities of the positron and the ion are balanced. The present work may have some relevance for laboratory/astrophysical e-p-i plasmas.
The gyrokinetic stability of electron-positron plasmas contaminated by ion (proton) admixture is studied in slab geometry. The appropriate dispersion relation is derived and solved. The ion-temperature-gradient driven instability, the electron-temperature-gradient driven instability, the universal mode, and the shear Alfven wave are considered. The contaminated plasma remains stable if the contamination degree is below some threshold, and it is found that the shear Alfven wave can be present in a contaminated plasma in cases where it is absent without ion contamination.
We investigate the nature of dissipative instability appearing in a prominence planar thread filled with partially ionised plasma in the incompressible limit. The importance of partial ionisation is investigated in terms of the ionisation factor and wavelength of waves propagating in the slab. To highlight the role of partial ionisation, we have constructed models describing various situations we can meet in solar prominence fine structure. Matching the solutions for the transversal component of the velocity and total pressure at the interfaces between the prominence slab and surrounding plasm…
Tearing Stability Prediction Combining Toroidal Calculations With a Two-Fluid Slab Layer
本文提出了一种结合环形计算与双流板层的撕裂稳定性预测方法，通过SLAYER和STRIDE代码有效评估等离子体稳定性，为托卡马克装置的设计和安全运行提供支持。
A new model for the joint neutrino flavor and plasma oscillations is introduced, in terms of the dynamics of the neutrino flavor polarization vector in a plasma background. Fundamental solutions are found for both time-invariant and time-dependent media, considering slow and fast variations of the electron plasma density. The model is shown to be described by a generalized Hamiltonian formalism. In the case of a broad spectrum of electron plasma waves, a statistical approach indicate the shift of both equilibrium value and frequency oscillation of flavor coherence, due to the existence of a tu…
Particle-in-cell (PIC) simulation results of sustained acceleration of electron-positron (e+e-) plasmas by comoving electromagnetic (EM) pulses are presented. When a thin slab of overdense e+e- plasma is irradiated with linear-polarized ultra-intense short laser pulses from both sides, the pulses are transmitted when the plasma is compressed to thinner than ~ 2 relativistic skin depths. A fraction of the plasma is then captured and efficiently accelerated by self-induced JxB forces. For 1 micron laser and 1021Wcm-2 intensity, the maximum energy exceeds GeV in a picosecond.
Mode Coupling and Breathing Oscillation in Partially Magnetized Cross-Field Plasmas
该研究探究部分磁化交叉场等离子体中呼吸振荡起始时旋转辐条的模式耦合，证实二者存在非线性耦合，提出角向振荡电场为电离供能，指出间歇性三波耦合是触发低频呼吸振荡的可能机制。
In this work, we suggest an easy-to-code higher-order finite volume semi-discrete scheme to analyze the nonlinear behavior of the electron-plasma oscillations by solving electron fluid equations numerically. The present method employs a fourth-order accurate centrally weighted essentially nonoscillatory reconstruction (CWENO4) polynomial for estimating the numerical flux at the grid-cell interfaces, and a fourth-order Runge-Kutta method for the time integration. The numerical implementation is validated by reproducing earlier results for both non-dissipative and dissipative cold plasmas. The s…
Modification of the resistive tearing instability with Joule heating by shear flow
本研究利用开源磁流体力学光谱工具Legolas，探究了剪切流对两种可压缩等离子体片构型中含焦耳热的线性电阻性撕裂不稳定性的影响，发现多磁零面下剪切流会改变撕裂行为，且增长率存在偏离解析标度律的区间，凸显了数值研究的必要性。
The conversion of an ordinary wave to an extraordinary wave in a 2D inhomogeneous slab model of the plasma confined by a sheared magnetic field is studied analytically.
We develop a method for investigating the relationship between the shape of a 1-particle distribution and non-linear electrostatic oscillations in a collisionless plasma, incorporating transverse thermal motion. A general expression is found for the maximum sustainable electric field, and is evaluated for a particular highly anisotropic distribution.
We consider the collective neutrino plasma interactions, and study the electron plasma instabilities produced by a nearly mono-energetic neutrino beam in a plasma. We describe the mutual influence of neutrino flavor oscillations and electron plasma waves. We show that the neutrino flavor oscillations are not only perturbed by electron plasmas waves, but also contribute to the dispersion relation and the growth rates of neutrino beam instabilities.
A classical model of radiation reaction for the betatron oscillation of an electron in a plasma wakefield accelerator is presented. The maximum energy of the electron due to the longitudinal radiation reaction is found, and the betatron oscillation damping due to both the longitudinal and transverse radiation reaction effects is analyzed. Both theoretical and numerical solutions are shown with good agreements. The regime that the quantum radiation takes effect is also discussed. This model is important for designing future plasma based super accelerators or colliders.
A first-principle study of the collective oscillation spectrum of a strongly correlated one-component plasma in a strong magnetic field is presented. The spectrum consists of six fundamental modes which are found to be in good agreement with results from the Quasi-Localized Charge approximation. At high frequencies additional modes are observed that include Bernstein-type oscillations and their transverse counterparts which are of importance for the high-frequency optical and transport properties of these plasmas.
Two dimensional modelling of the interaction between electromagnetic waves and plasma-metamaterial composite structures using the particle-in-cell method
本研究将电磁波在过密等离子体-超材料复合材料中传播的一维研究扩展至两维，通过PIC数值模拟发现该复合结构能有效阻挡电磁波形成驻波，为热沉积、微加工及隐身衣等应用提供基础。
Non-uniformity of the solar atmosphere along with the presence of non-adiabatic processes such as radiation cooling and unspecified heating can significantly affect the dynamics and properties of magnetoacoustic (MA) waves. To address the co-influence of these factors on the dispersion properties of MA waves, we considered a single magnetic slab composed of the thermally active plasma. Using the perturbation theory, we obtained a differential equation that determines the dynamics of the two-dimensional perturbations. Applying the assumption of strong magnetic structuring, we derived the disper…
Nonlinear plasma oscillations in an arbitrary mass ratio cold plasma have been studied using 1-D particle-in-cell simulation. In contrast to earlier work for infinitely massive ion plasmas it has been found that the oscillations phase mix away at any amplitude and that the rate at which phase mixing occurs, depends on the mass ratio ($Δ= m_{-}/m_{+}$) and the amplitude. A perturbation theoretic calculation carried upto third order predicts that the normalized phase mixing time $ω_{p-} t_{mix}$ depends on the amplitude $A$ and the mass ratio $Δ$ as $\sim [(A^{2}/24)(Δ/\sqrt{1 + Δ})]^{-1/3}$. We…
Previously developed method for finding asymptotic solutions of Vlasov equations using two-dimensional (in coordinate x and time t) Laplace transform is applied to low-collision electron-ion plasmas. Taking into account Coulomb collisions in the limit m_e << m_i, \bar{v_i} << \bar{v_e}, and T_e m_e << T_i m_i, results in the expression for longitudinal high-frequency plasma-electron oscillation/wave decrement essentially depending on oscillation frequency ω. This expression is quite different from the used one for low-frequency plasma sound, which can be derived using expansion in asymptotical…
An alternative explanation to the mechanism behind self-sustained oscillations of ions in direct current (DC) glow discharges is provided. Such description is distinguished from the one provided by the fluid models, where oscillations are attributed to the positive feedback mechanism associated with photoionization of particles and photoemission of electrons from the cathode. Here, oscillations arise as consequence of interaction between an ion and the surface charges induced by it at the bounding electrodes. Such mechanism provides an elegant explanation to why self-sustained oscillations occ…
The generation of electron surface oscillations in overdense plasmas irradiated at normal incidence by an intense laser pulse is investigated. Two-dimensional (2D) particle-in-cell simulations show a transition from a planar, electrostatic oscillation at $2ω$, with $ω$ the laser frequency, to a 2D electromagnetic oscillation at frequency $ω$ and wavevector $k>ω/c$. A new electron parametric instability, involving the decay of a 1D electrostatic oscillation into two surface waves, is introduced to explain the basic features of the 2D oscillations. This effect leads to the rippling of the plasma…
Methods of plasma heating by electromagnetic waves, interaction of electro-magnetic waves with magnetoactive plasma, plasma turbulence and transport processes are investigated in the trap of the linear plasma device OMT2. An ultrahigh frequency (UHF) contactless method is used to fill the open magnetic trap by plasma. We propose a new method of open magnetic trap filling with plasma whereby plasma is injected in the trap along the magnetic field from an independent stationary UHF source. The source is located outside the trap and plasma formation in it takes place in the strongly nonuniform ma…
We present a derivation of the dispersion relation for electrostatic oscillations (ESOs) in a zero temperature quantum plasma. In the latter, degenerate electrons are governed by the Wigner equation, while non-degenerate ions follow the classical fluid equations. The Poisson equation determines the electrostatic wave potential. We consider parameters ranging from semiconductor plasmas to metallic plasmas and electron densities of compressed matter such as in laser-compression schemes and dense astrophysical objects. Due to the wave diffraction caused by overlapping electron wave function due t…
The formulation of the Lifshitz formula in terms of real frequencies is reconsidered for half spaces described by the plasma model. It is shown that besides the surface modes (for the TM polarization), and the photonic modes, also waveguide modes must be considered.
The self-excitation of plasma series resonance (PSR) oscillations is a prominent feature in the current of low pressure capacitive radio frequency (RF) discharges. This resonance leads to high frequency oscillations of the charge in the sheaths and enhances electron heating. Up to now, the phenomenon has only been observed in asymmetric discharges. There, the nonlinearity in the voltage balance, which is necessary for the self-excitation of resonance oscillations with frequencies above the applied frequencies, is caused predominantly by the quadratic contribution to the charge-voltage relation…
The boundary problem about behavior (oscillations) of the electronic plasmas with arbitrary degree of degeneration of electronic gas in half-space with specular boundary conditions is analytically solved. The kinetic equation of Vlasov--Boltzmann with integral of collisions of type BGK (Bhatnagar, Gross, Krook) and Maxwell equation for electric field are applied. Distribution function for electrons and electric field in plasma in the form of expansion under eigen solutions of the initial system of equations are received. Coefficients of these expansions are found by means of the boundary condi…
The boundary problem about behaviour (oscillations) of the electronic plasmas with arbitrary degree of degeneration of electronic gas in half-space with diffusion boundary conditions is analytically solved. The kinetic equation of Vlasov - Boltzmann with integral of collisions of type BGK (Bhatnagar, Gross, Krook) and Maxwell equation for electric field are applied. Distribution function for electrons and electric field in plasma in the form of expansion under eigen solutions of the initial system of equations are received. Coefficients of these expansions are found by means of the boundary co…
Three dimensional rotatory modes of oscillations in a one-dimensional chain of rodlike charged particles or dust grains in a plasma are investigated. The dispersion characteristics of the modes are analyzed. The stability of different equilibrium orientations of the rods, phase transitions between the different equilibria, and a critical dependence on the relative strength of the confining potential are analyzed. The relations of these processes with liquid crystals, nanotubing, and plasma coating are discussed.
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